Probability Formula

ProbabilityBasicsVocabulary → Probability Formula

The probability of an event can be calculated by the proportion (or probability) formula

\textrm{Probability}=\frac{\textrm{Favorable events}}{\textrm{Total events}}

or

P=\frac{r}{n}

For example, in the basic probability vocabulary page, the question was,

Example
A coin is tossed two times. What is the probability that both times the head was occurred?

Answer
Here, the sample space is

S.S=\{HH,HT,TH,TT\}

And, the favorable event, or an event for which we want to find probability is HH. This event is 1 among the total 4 events. Hence, r=1 and n=4. The probability that both of the events are “heads” is thus

P(HH)=\frac{1}{4}=0.25

EXAMPLE 2
A fair dice is rolled once. What is the probability that an even number is occurred?

Answer
If a dice is rolled, any number from 1 to 6 can occur. So, the sample space is

S.S=\{1,2,3,4,5,6\}

And even numbers are three: 2,4,6. So favorable events (r) are 3, and total events (n) are 6. Hence,

P(\textrm{even number})=\frac{3}{6}=0.5